Is Private Language Possible?

21 Jul 2025

This post was machine translated and has not yet been proofread. It may contain minor errors or unnatural expressions. Proofreading will be done in the near future.

In the previous post, I examined the Kripke-Wittgenstein paradox. To summarise, the Kripke-Wittgenstein paradox is based on the consideration that there are no normative facts encompassing the infinite cases in which a particular word can be used. From this, Kripke-Wittgenstein draws the following conclusion:

“Speaker A means M by symbol s” corresponds to no fact.

According to Kripke’s reading, Wittgenstein offers a “sceptical solution” to this conclusion. That is, he accepts the above conclusion as it stands—there is no fact corresponding to “Alice means addition by ‘+’“—whilst explaining how it can be used meaningfully, unlike “Alice’s thoughts are green”. The gist of the explanation is to emphasise the publicity of language: the meaning of language is inextricably linked to the function it has in the community, and therefore discussions of meaning are vacuous at the level of individual speakers but valid at the community level.

1. From the Tractus to the Investigations

Kripke belongs to the so-called “traditional interpretation” school, which sees a stark difference between early Wittgenstein, symbolised by the Tractatus Logico-Philosophicus, and later Wittgenstein, symbolised by the Philosophical Investigations. Kripke summarises the characteristics of the view of language presented in the Tractus as follows:

• Logical atomism. All meaningful propositions are analysed as logical compositions of atomic propositions.
• Picture theory. Atomic propositions and the states of affairs they represent correspond to each other like pictures. When the state of affairs represented by an atomic proposition obtains, the proposition is true.
• Truth-conditional theory. The meaning of a proposition lies in its truth conditions—that is, what state of affairs corresponds to that proposition.
• A priori approach. The characteristics of language outlined above can be inferred through a priori reasoning.

By contrast, Kripke analyses that the Investigations reveals two views of language that contrast with the Tractus.

• Assertability-conditional theory. The meaning of a proposition lies in its assertability conditions—that is, in what circumstances the proposition can be asserted or rejected.¹
• Pragmatism. Consideration of what role or function asserting or rejecting a particular proposition plays in our lives is central to a proper understanding of language.²

Here, assertability-conditional theory can be found in other philosophical positions even before Wittgenstein. Brouwer’s intuitionist mathematics and logical positivism’s verificationism are representative examples. Kripke sees Wittgenstein’s originality as lying in the second characteristic, namely pragmatism. Wittgenstein criticises the word-object correspondence demanded by Frege and others, urging instead that we consider the actual situations in which words are used. To take numbers as an example, Frege argues that there must be objects to which numbers refer.³ However, Wittgenstein mentions actual situations in which numbers are used—counting goods in the marketplace, teachers counting students—and emphasises that in these situations, if the alphabet had been recited instead of numbers, the purpose of the linguistic act would still have been achieved. In short, numbers are not, as Frege would have it, “language that refers to natural numbers” but “language that engages in the activity of counting things”.

2. The Sceptical Solution

From the perspective of Wittgenstein’s later view of language based on assertability-conditional theory, the sceptical argument does not immediately suggest that “Alice means addition by ‘+’” is meaningless. Even if there is no state of affairs corresponding to the proposition, the existence of a state of affairs is not—unlike the truth-conditional view of language—a necessary condition for a proposition to be meaningful.

On the other hand, pragmatism provides a separate necessary condition for “Alice means addition by ‘+’” to be regarded as a meaningful proposition. That is, the proposition must play a useful role in the language game. Kripke explains the role played by this proposition in connection with another thought experiment that appears in the Investigations, the “private language argument”. But before that, let us consider the characteristics of Wittgenstein’s sceptical solution in comparison with the scepticism of Berkeley and Hume.

2.1. Berkeley’s Scepticism

By the expression “sceptical solution”, Kripke collectively refers to arguments with the following characteristics:

1. Present a proposition P that we consider self-evident.
2. Present a “sceptical paradox” that claims that proposition P is in fact contradictory, incomprehensible, or unjustifiable.
3. Nevertheless, explain why we can regard P as a legitimate proposition in everyday life by reinterpreting the meaning of P, despite the sceptical paradox.
4. As a bonus, one can propagate that the meaning of P reinterpreted in 3 is the “real meaning”, the “meaning of ordinary people”, and that the meaning of P rejected in 2 is the “false meaning”, the “meaning misled by philosophers”.

Consider, for example, Berkeley’s idealism. Berkeley points out that what an individual can perceive is only the mental images that occur within him. Therefore, we can never prove the independent existence of ‘external objects’. This is because inferring the existence of external objects from a collection of internal mental images cannot be logically justified. To outline this in accordance with the three stages presented above:

1. We regard the proposition “There is an apple in my hand” as legitimate.
2. However, since what an individual can perceive is limited to internal mental images, the proposition in 1 cannot be justified.
3. Nevertheless, the reason we can regard the proposition in 1 as a legitimate proposition is that the real meaning of the proposition in 1 is actually “I am experiencing red visual sensations, sour olfactory sensations, spherical hard tactile sensations, etc.”

(Kripke clearly shows his distaste for this kind of argument in the original paper. In my view, this may stem from resentment at the way American functionalist philosophers have—in Kripke’s view—unjustifiably pushed such “sceptical solutions”.)

2.2. Hume’s Scepticism

As another example, consider Hume’s scepticism about causation. Hume asks whether there is empirical evidence for the proposition “Event A is the cause of event B” that can be presented beyond “Event A and event B occurred in succession”. Such evidence would consist of observations of causal nexuses that actually exist in nature, but Hume points out that observations of such nexuses are beyond the realm of human experience. What we can experience is only regularities of events. That is, when we observe several times that when an event token belonging to event type A occurs, an event token belonging to event type B occurs, we say that causation obtains between types A and B.

Kripke points out that the conclusion of Hume’s causal scepticism is the impossibility of private causation. If, as Hume argues, causation is a statement about regularities between two event types, then it is meaningless to discuss causation for event tokens that are so peculiar that they cannot even be typed. For example, the proposition “Helium was generated by the collision of a meson and a trion” is meaningful as a statement that there are several particle tokens corresponding to the types “meson”, “trion”, and “helium”, and that regularity was discovered by colliding these particles repeatedly. However, if there are particles X and Y that exist only once in the universe, then even if particle Z were generated by colliding them, we could not say “Z was generated because of the collision of X and Y”. All we can say is “Z was generated immediately after the collision of X and Y”.

Kripke suggests reading Wittgenstein’s private language argument with Hume’s argument in mind. According to Kripke’s reading, the flow of arguments between Wittgenstein and Hume is very similar.

3. The Private Language Argument

3.1. Traditional Interpretation

Now let us examine the private language argument proper. Wittgenstein presents the following case in the Investigations. Alice has difficulty expressing a particular emotion she feels in language. So she gives that emotion the name ‘S’ and writes “feeling S” in her diary whenever she feels that emotion. After several years, Alice feels that she has become familiar with the use of ‘S’. Here Wittgenstein poses a question. Can we say that Alice has given her own meaning to the symbol ‘S’, that is, that she has formed a private language?

Wittgenstein’s answer is negative. However, as Kripke also points out, Wittgenstein’s reasons for rejecting private language were puzzling to interpreters. The most standard interpretation is as follows. The reason Wittgenstein argues that private language is impossible is that an individual alone cannot receive confirmation that he is using this symbol correctly. For instance, Alice can escape from scepticism about whether the emotion she calls ‘S’ today really matches the emotion she called ‘S’ years ago. The only way Alice can escape from solipsistic scepticism is to belong to a linguistic community that uses unified symbols and receive confirmation from them that her use of symbols is correct.

However, this argument is, as numerous scholars including Ayer have long pointed out, extremely flimsy. For instance, when I am uncertain whether I may now call my emotion ‘happiness’, does receiving confirmation from others saying “You are indeed happy now” improve the situation? How can we be certain that their judgement is correct? Rather, the reverse argument that “Even if others tell me that I am now in a state of happiness, I cannot be certain that their judgement is really correct, so I myself must check my inner state” is more plausible. Moreover, considering that community confirmation is also ultimately received through an individual’s private senses, including sight and hearing, there is essentially no difference between an individual checking his own inner state and receiving confirmation from the community.

3.2. Kripke’s Interpretation

However, Kripke argues that understanding the private language argument in this way is a misunderstanding. Wittgenstein’s intention is not to banish private language to the realm of impossibility. Rather, according to the sceptical paradox, all language—whether private or public—is impossible. Wittgenstein seeks to rescue the possibility of language in response to this. Because the strategy of this rescue appeals to the publicity of language, private language remains in the realm of impossibility.

Wittgenstein’s “solution” to the sceptical paradox can be understood by considering the following three cases. The first is the case where Alice is the only person in this universe who uses the ‘+’ symbol. Alice uses ‘+’ according to her own inclination towards ‘+’ (of course, this is a tautological statement). From time to time Alice will make calculation errors with ‘+’, and in extreme cases when she is under the influence of drugs, she may use ‘+’ in bizarre ways like quaddition. But in all cases Alice will believe that she is using ‘+’ according to legitimate rules. And according to the Kripke-Wittgenstein paradox, there are no facts that refute Alice’s belief, so this is all that can be said about Alice’s use of ‘+’. To borrow Kripke’s words:

It is part of our language game of speaking of rules that a speaker may, without ultimately giving any justification, follow his own confident inclination that this way (say, responding ‘125’) is the right way to respond, rather than another way (e.g. responding ‘5’). That is, the ‘assertability conditions’ that license an individual to say that, on a given occasion, he ought to follow his rule this way rather than that are, ultimately, that he does what he is inclined to do. […] All we can say, if we consider a single person in isolation, is that our ordinary practice licenses him to apply the rule in the way it strikes him.

(Italics are the original emphasis, bold is my emphasis. The statement “It is part of our language game of speaking of rules that a speaker may say…” can be understood by analogy to “Castling is part of chess”, showing that such statements are no different from part of the definition of the language game of ‘speaking of rules’. That is, a language game in which such speech is not possible cannot be called the language game of ‘speaking of rules’.)

But as Kripke points out, this is not what we expect from the language game of ‘speaking of rules’. For instance, imagine someone playing chess alone against a wall. He sets a chess clock for one hour and makes the first move as white, then waits for his “opponent”, the wall, to respond. But the “opponent” does not respond and loses by timeout after an hour. Therefore white always wins. Let us call this private chess. Private chess satisfies all the rules of chess, but it is not chess at all. At least, it is not the chess we expect. In normal chess, white must be able to lose. Similarly, private rules, even if they satisfy the rules of the ‘rule-speaking’ language game, are not the ‘rule-speaking’ language game we expect. In the normal ‘rule-speaking’ language game, the speaker must be able to make mistakes in following rules.

Now let us move on to the next case. The second is the case where Alice and Smith are the two people in this universe who use the ‘+’ symbol. Their inclinations towards ‘+’ may match or diverge. If Alice answers ‘125’ and Smith answers ‘5’ to ‘68 + 57’, Alice will point out that Smith is not using ‘+’ according to the correct rule. However, this pointing out is something Smith can also do to Alice. And according to the Kripke-Wittgenstein paradox, there are no facts corresponding to which of their pointings out is more correct, so this is all that can be said about their use of ‘+’.

Finally, there is the case where those who use the ‘+’ symbol in this universe form a sufficiently large community, not just Alice. In this case, although there may initially be speakers who use ‘+’ in ways that conflict with the community, these speakers will gradually disappear from the community because they interfere with the function that the ‘+’ symbol performs in the community (here the reason why Wittgenstein values pragmatic considerations becomes apparent). For example, one of the functions of ‘+’ is to manage accounts. However, people who use ‘+’ like quaddition will manage accounts in a non-standard way, which gives those who use ‘+’ like addition reason not to delegate the use of ‘+’ to them any longer. In this way, the sustained process of approval and expulsion based on linguistic function converges to a community of speakers who follow consistent rules. Thus “Alice means addition by ‘+’” is useful as an expression that the community approves of Alice’s use of ‘+’, and therefore meaningful.

Note that what Kripke calls inversion of a conditional is employed here as a philosophical technique. Inversion of a conditional means asserting “if not Q then not P” instead of the proposition “if P then Q”. Of course, the two conditionals are contrapositives and therefore extensionally equivalent, but they differ in setting the priority between P and Q. In the former case, the obtaining of P determines the obtaining of Q, whereas in the latter case, the obtaining of Q determines the obtaining of P.

According to the traditional view of language, the fact that speakers use the same symbol in the same way is explained by the fact that they assign the same meaning to that symbol. According to this view, the following conditional obtains:

Alice means addition by ‘+’ -> Alice answers ‘125’ to ‘68 + 57’

However, the sceptical solution inverts this conditional as follows:

Alice does not answer ‘125’ to ‘68 + 57’ -> Alice does not mean addition by ‘+’

More precisely, considering that the sceptical solution is based on assertability conditions rather than truth conditions:

Alice does not answer ‘125’ to ‘68 + 57’ -> In the context of the language game of ‘speaking of rules’, we cannot say “Alice means addition by ‘+’”.

Of course, we would not immediately draw the extreme conclusion that Alice does not mean addition by ‘+’ simply because she did not answer ‘125’ to ‘68 + 57’. We would probably think that Alice made a calculation error. However, if Alice uses the ‘+’ symbol in a very unacceptable way, such as answering ‘5’ to ‘68 + 57’, we would withdraw the statement that she means addition by ‘+’.

In short, Kripke-Wittgenstein understands the process by which the language game of ‘speaking of rules’ transforms from a trivial language game to a useful language game as an emergent process through community.

4. Characteristics of the Sceptical Solution

4.1. Form of Life

The legitimacy of the sceptical solution is based on the fact that language users converge on performing the same operation, namely addition, with ‘+’. If individuals each gave different answers to ‘68 + 57’—A giving 125, B giving 7, C giving 58—the sceptical solution could not obtain.

According to Kripke’s reading, Wittgenstein calls the agreement we show in the use of symbols (answering ‘125’ to ‘68 + 57’) and the series of activities thereby made possible (thus being able to pay for a computer costing £125,000 in instalments of £68,000 and £57,000) a “form of life”. According to Wittgenstein, the reason we can give the consistent answer ‘125’ to ‘68 + 57’ is not because we mean the same operation, namely addition, by ‘+’. Rather, the reason we can say that we mean addition by ‘+’ is that we are participating in a language game based on a common form of life. In Wittgenstein’s analysis, the fact that we give the consistent answer ‘125’ to ‘68 + 57’ is simply a given fact, not a phenomenon to be explained.

(Personal note: Compare Kripke’s footnote 76 with the logical alien thought experiment.)

76. Can we imagine forms of life other than our own, that is, can we imagine creatures who follow rules in bizarre quus-like ways? It seems to me that there may be a certain tension in Wittgenstein’s philosophy here. On the one hand, it would seem that Wittgenstein’s paradox argues that there is no a priori reason why a creature could not follow a quus-like rule, and thus in this sense we ought to regard such creatures as conceivable. On the other hand, it is supposed to be part of our very form of life that we find it natural and, indeed, inevitable that we follow the rule for addition in the particular way that we do. (See §231: ““But surely you can see . . . ?” That is just the characteristic expression of someone who is under the compulsion of a rule.”) But then it seems that we should be unable to understand ‘from the inside’ (cf. the notion of ‘Verstehen’ in various German writers) how any creature could follow a quus-like rule. We could describe such behaviour extensionally and behaviouristically, but we would be unable to find it intelligible how the creature finds it natural to behave in this way. This consequence does, indeed, seem to go with Wittgenstein’s conception of the matter.

Of course we can define the quus function, introduce a symbol for it, and follow the appropriate rule for computing its values. I have done so in this very essay. What it seems may be unintelligible to us is how an intelligent creature could get the very training we have for the addition function, and yet grasp the appropriate function in a quus-like way. If such a possibility were really completely intelligible to us, would we find it so inevitable to apply the plus function as we do? Yet this inevitability is an essential part of Wittgenstein’s own solution to his problem.

The point is even stronger with respect to a term like ‘green’. Can we grasp how someone could be presented with a number of green objects, and be told to apply the term ‘green’ just to ‘things like these’, and yet apply the term learnt as if it meant ‘grue’? It would seem that if we find our own continuation to be inevitable, in some sense we cannot.

4.2. External Criteria for Psychological Phenomena

The sceptical solution that agreement in the use of symbols is the very content of the statement that a speaker uses that symbol with a particular meaning leads to the following statement by Wittgenstein about the philosophy of mind:

“An ‘inner process’ stands in need of outward criteria.” (§580)

Consider the case where a young child learns the two words ‘table’ and ‘hurt’. In the former case, if the child points to a table and says ‘table’, the parents will approve the utterance, and if they point to a chair and say ‘table’, they will tell them it is wrong. Through this process, the child comes to agree with the linguistic community in the use of the symbol ‘table’. However, in the case of ‘hurt’, this is impossible. The child cannot directly reveal the emotion they experience to receive confirmation that this corresponds to ‘hurt’. Instead, the child will show external behaviour such as bursting into tears or frowning, and based on that behaviour, the parents will decide whether the child’s utterance of ‘hurt’ is legitimate. If this is the meaning of §580, then §580 is not—as traditionally considered—a premise that Wittgenstein prepares for the private language argument, but rather an implication of the sceptical paradox, just like the private language argument.

In this regard, Kripke presents both liberal and strict interpretations of §580. If §580 is interpreted strictly, each expression belonging to psychological language must have a natural expression associated with that expression. For example, the natural expression associated with pain is grimacing. Therefore, if a child learning language grimaces and says “Ow!”, we approve it. In this way, all psychological expressions have natural behaviours associated with them, and the observability of these behaviours prevents these expressions from degenerating into private language.

However, Kripke presents a more liberal interpretation. According to this, what requires external criteria is not individual psychological expressions but “psychological language” itself. Kripke sees this as a more accurate consideration of how psychological language operates. If there is a speaker who shows sufficient mastery of psychological expressions that have clear external criteria—for instance, pain—we judge that they have mastered psychological language in general, and therefore, if they state that they have grasped a particular emotion or quale in their inner state, even if that emotion and quale have no external criteria, we acknowledge that statement as legitimate. (In my view, “I have consciousness” would seem to be an example of such a statement.)

For this, see footnotes 81, 82, and 83 in the main text. (Incidentally, these three footnotes are substantial enough to constitute a section on their own…)

4.3. Is the Sceptical Solution Circular?

At the end of the paper, Kripke warns that the sceptical solution can be misunderstood as follows:

That a linguistic community means addition by ‘+’ is that the majority of members of that community use ‘+’ as addition.

Or, more precisely:

That the operation a linguistic community means by ‘+’ is f means that the majority of members of that community answer f(x, y) to ‘x + y’.

According to Kripke, this is a mistaken understanding. The sceptical solution interpreted in this way is virtually no different from a dispositional analysis at the community level, and therefore has—if not all, then at least some of—the difficulties faced by dispositional analysis. Moreover, the above interpretation provides truth conditions for “a linguistic community means … by …”. This fundamentally misses Wittgenstein’s project of moving from truth-conditional theory to assertability-conditional theory.

Kripke emphasises that Wittgenstein’s sceptical solution does not seek to provide new truth conditions for “a linguistic community means … by …” but merely focuses on the environment that makes such statements possible and the advantages gained by using such statements. To quote from the text:

What follows from these assertability conditions is not that the answer everyone gives to an addition problem is, by definition, the correct one, but rather the platitude that, if everyone agrees upon a certain answer, then no one will feel justified in calling the answer wrong.

Kripke probably (accurately) predicted that this passage would be the subject of much criticism. So he later added a long footnote 87. Footnote 87 is a sketch of an explanation against the criticism that Wittgenstein’s sceptical solution is circular or still falls into the infinite regress of scepticism.

87. If Wittgenstein had been attempting to give a necessary and sufficient condition to show that ‘125’, not ‘5’, is the ‘right’ response to ‘68+ 57’, he might be charged with circularity. For he might be taken to say that my response is correct if and only if it agrees with that of others. But even if the sceptic and I both accept this criterion in advance, might not the sceptic maintain that just as I was wrong about what ‘+’ meant in the past, so I was wrong about ‘agree’? Indeed, to attempt to reduce the rule for addition to another rule - “Respond to an addition problem exactly as others do!” - falls foul of Wittgenstein’s strictures on ‘a rule for interpreting a rule’ just as much as any other such attempted reduction. Such a rule, as Wittgenstein would emphasise, also describes what I do wrongly: I do not consult others when I add. (We wouldn’t manage very well, if everyone had to follow a rule of the proposed form - no one would respond without waiting for everyone else.)

What Wittgenstein is doing is describing the utility in our lives of a certain practice. Necessarily he must give this description in our own language. As in the case of any such use of our language, a participant in another form of life might apply various terms in the description (such as “agreement”) in a non-standard ‘quus-like’ way. Indeed, we may judge that those in a given community ‘agree’, while someone in another form of life would judge that they do not. This cannot be an objection to Wittgenstein’s solution unless he is to be prohibited from any use of language at all.

However, several questions still remain. First, there remains a question about whether Kripke’s defence that “This cannot be an objection to Wittgenstein’s sceptical solution” is valid. Second, even if the intention of the sceptical solution is not to provide truth conditions for meaning statements (the answer everyone gives to a particular addition problem is the correct answer) but to describe the function of meaning statements (if everyone agrees upon a certain answer, then no one will feel justified in calling the answer wrong), questions may remain about whether the latter description is correct. That is, if everyone really agrees upon a certain answer, will no one feel justified in calling the answer wrong? Regarding this, let us look at Kripke’s following footnote:

Does it make any sense to doubt whether a response we all agree upon is ‘correct’? Clearly in some cases an individual may doubt whether the community may correct, later, a response it had agreed upon at a given time. [Author’s note: Think of the community’s change of position on “adultery is a crime”] But may the individual doubt whether the community may not in fact always be wrong, even though it never corrects its error? It is hard to formulate such a doubt within Wittgenstein’s framework, since it looks like a question, whether, as a matter of ‘fact’, we might always be wrong; and there is no such fact.

However, this does not mean that Kripke-Wittgenstein attributes full authority over the rules of meaning solely to the community. In the following footnote, Kripke leaves a clause guaranteeing the realm of autonomy that individuals have in meaning and rule-following:

On the other hand, within Wittgenstein’s framework it is still true that, for me, no assertions about community responses for all time need establish the result of an arithmetical problem; that I can legitimately calculate the result for myself, even given this information, is part of our ‘language game’. [Author’s note: Compare this with Asch’s conformity experiments.]

The reader will probably be confused about what exactly Kripke is trying to say. The problem is that I too am very confused. And in my view, Kripke himself seems to have felt confusion about this point. Kripke’s footnote concludes with the following admission:

I feel some uneasiness may remain regarding these questions. Considerations of time and space, as well as the fact that I might have to abandon the role of advocate and expositor in favour of that of critic, have led me not to carry out a more extensive discussion.

To summarise the key points:

1. It is wrong to understand the sceptical solution as follows: The necessary and sufficient condition for “‘125’ is the right answer to ‘68 + 57’” to be true is that the community shows a unanimous answer of ‘125’ to ‘68 + 57’.

2. The sceptical solution should be understood as follows: The necessary and sufficient condition for “‘125’ is the right answer to ‘68 + 57’” to be accepted within the community is that the community shows a unanimous answer of ‘125’ to ‘68 + 57’.

   • Put differently, if the community shows a unanimous answer of ‘125’ to ‘68 + 57’, then the utterance “‘125’ is the wrong answer to ‘68 + 57’” will not be legitimately accepted in that community.

3. The following questions can be raised about 2:

   1. It is unclear why 1 is circular but 2 is not circular.
   2. In some cases, it seems that an individual can legitimately raise questions about whether an answer is really correct even in situations where the community shows a unanimous answer.

These questions were explained somewhat unclearly in Kripke’s original paper, and indeed the criticisms subsequently raised against the sceptical solution focus on these questions. I shall try to organise these in a separate post if the opportunity arises in the future.

---